Ghost operators, expanders, and exactness II

Rufus Willett (University of Hawaii)

Thursday 12th June, 2014 17:30-18:30 Maths 516

Abstract

Associated to a discrete metric space X (for example, the natural numbers, or integers) is an algebra of ‘finite width’, or
‘band’ matrices with bounded entries acting on the Hilbert space l

²

(X).  In the first lecture, I’ll discuss so-called ghost operators
on X - those with matrix entries tending to zero at infinity - and how expansion-type conditions on X allow non-trivial examples to exist as
norm limits of band operators.

In the second lecture, I’ll discuss other representations of the algebra of band matrices arising from metric ultralimits.  I’ll
explain what ghosts have to do with exactness in the sense of C*-algebra theory, and sketch applications to K-theory and Baum-Connes
type conjectures (without assuming any prior knowledge of exactness or K-theory).

Some of these lectures draw on joint work with Paul Baum, Erik Guentner, John Roe, and Guoliang Yu.

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